The power of “mapping the territory”. Why economists should become more aware of the performativity of their models

Economics is not simply about representing reality; it is also about shaping it, an approach encapsulated in Donald MacKenzie’s aphorism that economics is best conceived as an “engine, not as a camera” (MacKenzie and Millo (Am J Sociol 109(1):107–145, 2003). The making and application of economic theories and models contribute actively and intentionally towards the making of our social world, by encouraging, guiding and legitimizing actions and decisions, or discouraging others, and by steering them in certain directions. It follows that economists do not simply draw maps of the economic territory within their compass: they are not straightforwardly the cartographers of the economy, and cannot be seen as the disinterested observers that they commonly represent themselves to be, and indeed are often thought of as. Their theoretical work has or aims at practical consequences for the economy, and indeed for society at large, and their interests and influence are thus by no means confined to academia alone. This article calls for a discussion of the ethical responsibilities of economists, and of economics, and challenges the discipline properly to assume those responsibilities; and it concludes by considering the key questions—what makes a ‘good’ economic model; and what criteria should be used to distinguish the good models, and the ‘good ways’ of handling models and their results, from the bad ones. As far as epistemology, the methodology of research programmes and the relation of theory and (social) practice are concerned, the insights of mainly von Hayek (Br J Philos Sci 6(23):209–225, 1955, The pretence of knowledge. Lecture to the memory of Alfred Nobel, 1974; Individualism and economic order, University of Chicago Press, Chicago, pp 33–56, 1980a; Individualism and economic order, University of Chicago Press, Chicago, pp 57–76, 1980b; The theory of complex phenomena. Readings in the philosophy of social science, MIT Press, Cambridge, 1994) and Popper (e.g. The myth of the framework: in defence of science and rationality, Routledge, New York 1994a; Models, instruments, and truth. The status of the rationality principle in the social sciences, pp 154–184, 1994b) provide the background of my discussion of the mentioned issues.     

An improved distributed data aggregation scheduling in wireless sensor networks

This paper focuses on the distributed data aggregation collision-free scheduling problem, which is one of very important issues in wireless sensor networks. Bo et al. (Proc. IEEE INFOCOM, 2009) proposed an approximate distributed algorithm for the problem and Xu et al. (Proc. ACM FOWANC, 2009) proposed a centralized algorithm and its distributed implementation to generate a collision-free scheduling for the problem, which are the only two existing distributed algorithms. Unfortunately, there are a few mistakes in their performance analysis in Bo et al. (Proc. IEEE INFOCOM, 2009), and the distributed algorithm can not get the same latency as the centralized algorithm because the distributed implementation was not an accurate implementation of the centralized algorithm (Xu et al. in Proc. ACM FOWANC, 2009). According to those, we propose an improved distributed algorithm to generate a collision-free schedule for data aggregation in wireless sensor networks. Not an arbitrary tree in Bo et al. (Proc. IEEE INFOCOM, 2009) but a breadth first search tree (BFS) rooted at the sink node is adopted, the bounded latency 61R+5Δ?67 of the schedule is obtained, where R is the radius of the network with respect to the sink node and Δ is the maximum node degree. We also correct the latency bound of the schedule in Bo et al. (Proc. IEEE INFOCOM, 2009) as 61D+5Δ?67, where D is a diameter of the network and prove that our algorithm is more efficient than the algorithm (Bo et al. in Proc. IEEE INFOCOM, 2009). We also give a latency bound for the distributed implementation in Xu et al. (Proc. ACM FOWANC, 2009).     

A Branch and Bound algorithm for general mixed-integer quadratic programs based on quadratic convex relaxation

Let \((MQP)\) be a general mixed-integer quadratic program that consists of minimizing a quadratic function \(f(x) = x^TQx +c^Tx\) subject to linear constraints. Our approach to solve \((MQP)\) is first to consider an equivalent general mixed-integer quadratic problem. This equivalent problem has additional variables \(y_{ij}\) , additional quadratic constraints \(y_{ij}=x_ix_j\) , a convex objective function, and a set of valid inequalities. Contrarily to the reformulation proposed in Billionnet et al. (Math Program 131(1):381–401, 2012), the equivalent problem cannot be directly solved by a standard solver. Here, we propose a new Branch and Bound process based on the relaxation of the non-convex constraints \(y_{ij}=x_ix_j\) to solve \((MQP)\) . Computational experiences are carried out on pure- and mixed-integer quadratic instances. The results show that the solution time of most of the considered instances with up to 60 variables is improved by our Branch and Bound algorithm in comparison with the approach of Billionnet et al. (2012) and with the general mixed-integer nonlinear solver BARON (Sahinidis and Tawarmalani, Global optimization of mixed-integer nonlinear programs, user’s manual, 2010).     

A new approximation algorithm for the Selective Single-Sink Buy-at-Bulk problem in network design

The Selective Single-Sink Buy-at-Bulk problem was proposed by Awerbuch and Azar (FOCS 1997). For a long time, the only known non-trivial approach to approximate this problem is the tree-embedding method initiated by Bartal (FOCS 1996). In this paper, we give a thoroughly different approximation approach for the problem with approximation ratio $O(\sqrt{q})$ , where q is the number of source terminals in the problem instance. Our approach is based on a mixed strategy of LP-rounding and the greedy method. When the number q (which is always at most n) is relatively small (say, q=o(log² n)), our approximation ratio $O(\sqrt{q})$ is better than the currently known best ratio O(logn), where n is the number of vertices in the input graph.     

Are there more almost separable partitions than separable partitions?

A partition of a set of n points in d-dimensional space into p parts is called an (almost) separable partition if the convex hulls formed by the parts are (almost) pairwise disjoint. These two partition classes are the most encountered ones in clustering and other partition problems for high-dimensional points and their usefulness depends critically on the issue whether their numbers are small. The problem of bounding separable partitions has been well studied in the literature (Alon and Onn in Discrete Appl. Math. 91:39–51, 1999; Barnes et al. in Math. Program. 54:69–86, 1992; Harding in Proc. Edinb. Math. Soc. 15:285–289, 1967; Hwang et al. in SIAM J. Optim. 10:70–81, 1999; Hwang and Rothblum in J. Comb. Optim. 21:423–433, 2011a). In this paper, we prove that for d≤2 or p≤2, the maximum number of almost separable partitions is equal to the maximum number of separable partitions.     

Valuing high technology growth firms

For the valuation of fast growing innovative firms Schwartz and Moon (Financ Anal J 56:62–75, 2000), (Financ Rev 36:7–26, 2001) develop a fundamental valuation model where key parameters follow stochastic processes. While prior research shows promising potential for this model, it has never been tested on a large scale dataset. Thus, guided by economic theory, this paper is the first to design a large-scale applicable implementation on around 30,000 technology firm quarter observations from 1992 to 2009 for the US to assess this model. Evaluating the feasibility and performance of the Schwartz-Moon model reveals that it is comparably accurate to the traditional sales multiple with key advantages in valuing small and non-listed firms. Most importantly, however, the model is able to indicate severe market over- or undervaluation from a fundamental perspective. We demonstrate that a trading strategy based on our implementation has significant investment value. Consequently, the model seems suitable for detecting misvaluations as the dot-com bubble.     

Acyclic edge coloring of planar graphs without a 3-cycle adjacent to a 6-cycle

An acyclic edge coloring of a graph \(G\) is a proper edge coloring such that no bichromatic cycles are produced. The acyclic chromatic index \(a'(G)\) of \(G\) is the smallest integer \(k\) such that \(G\) has an acyclic edge coloring using \(k\) colors. Fiam? ik (Math Slovaca 28:139–145, 1978) and later Alon et al. (J Graph Theory 37:157–167, 2001) conjectured that \(a'(G)\le \Delta +2\) for any simple graph \(G\) with maximum degree \(\Delta \) . In this paper, we confirm this conjecture for planar graphs without a \(3\) -cycle adjacent to a \(6\) -cycle.     

A primal-dual approximation algorithm for the Asymmetric Prize-Collecting TSP

We present a primal-dual ?log(n)?-approximation algorithm for the version of the asymmetric prize collecting traveling salesman problem, where the objective is to find a directed tour that visits a subset of vertices such that the length of the tour plus the sum of penalties associated with vertices not in the tour is as small as possible. The previous algorithm for the problem (V.H. Nguyen and T.T Nguyen in Int. J. Math. Oper. Res. 4(3):294–301, 2012) which is not combinatorial, is based on the Held-Karp relaxation and heuristic methods such as the Frieze et al.’s heuristic (Frieze et al. in Networks 12:23–39, 1982) or the recent Asadpour et al.’s heuristic for the ATSP (Asadpour et al. in 21st ACM-SIAM symposium on discrete algorithms, 2010). Depending on which of the two heuristics is used, it gives respectively 1+?log(n)? and $3+ 8\frac{\log(n)}{\log(\log(n))}$ as an approximation ratio. Our algorithm achieves an approximation ratio of ?log(n)? which is weaker than $3+ 8\frac{\log(n)}{\log(\log(n))}$ but represents the first combinatorial approximation algorithm for the Asymmetric Prize-Collecting TSP.     

Betriebsinterne Arbeitsmärkte, Hierarchien und Neueinstellungen: Eine empirische Untersuchung mit Personaldaten

Many empirical studies which deal with internal labour markets are related to the work of Doeringer and Piore (1971). The majority of these studies cannot find closed internal labour markets with entry positions at the lower end of a firm’s hierarchy. Most of these studies, however, use data from financial and service industries, managerial or other white-collar workers. Doeringer and Piore (1971) state that closed internal labour markets with clearly defined entry positions should be found especially for blue-collar workers in the manufacturing industry, because firm specific human capital is of large importance in these industries. In this paper, a large data set of a manufacturing company with blue-collar and white-collar workers is used. We show that the internal labour market of blue-collar workers is more closed than that of white-collar workers. Moreover, we find that firm specific human capital plays a major role in determining the hierarchical position of blue-collar workers. Entries of white-collar workers, however, appear at all hierarchical positions. Furthermore, formal education plays a major role in allocating the white-collar workers.     

Adjacent vertex distinguishing edge colorings of planar graphs with girth at least five

An adjacent vertex distinguishing edge coloring of a graph \(G\) is a proper edge coloring of \(G\) such that any pair of adjacent vertices admit different sets of colors. The minimum number of colors required for such a coloring of \(G\) is denoted by \(\chi ^{\prime }_{a}(G)\) . In this paper, we prove that if \(G\) is a planar graph with girth at least 5 and \(G\) is not a 5-cycle, then \(\chi ^{\prime }_{a}(G)\le \Delta +2\) , where \(\Delta \) is the maximum degree of \(G\) . This confirms partially a conjecture in Zhang et al. (Appl Math Lett 15:623–626, 2002).     

Improved approximation algorithms for the max-bisection and the disjoint 2-catalog segmentation problems

We consider the max-bisection problem and the disjoint 2-catalog segmentation problem, two well-known NP-hard combinatorial optimization problems. For the first problem, we apply the semidefinite programming (SDP) relaxation and the RPR² technique of Feige and Langberg (J. Algorithms 60:1–23, 2006) to obtain a performance curve as a function of the ratio of the optimal SDP value over the total weight through finer analysis under the assumption of convexity of the RPR² function. This ratio is shown to be in the range of [0.5,1]. The performance curve implies better approximation performance when this ratio is away from 0.92, corresponding to the lowest point on this curve with the currently best approximation ratio of 0.7031 due to Feige and Langberg (J. Algorithms 60:1–23, 2006). For the second problem, similar technique results in an approximation ratio of 0.7469, improving the previously best known result 0.7317 due to Wu et al. (J. Ind. Manag. Optim. 8:117–126, 2012).     

Some results on the target set selection problem

In this paper we consider a fundamental problem in the area of viral marketing, called Target Set Selection problem. We study the problem when the underlying graph is a block-cactus graph, a chordal graph or a Hamming graph. We show that if G is a block-cactus graph, then the Target Set Selection problem can be solved in linear time, which generalizes Chen’s result (Discrete Math. 23:1400–1415, 2009) for trees, and the time complexity is much better than the algorithm in Ben-Zwi et al. (Discrete Optim., 2010) (for bounded treewidth graphs) when restricted to block-cactus graphs. We show that if the underlying graph G is a chordal graph with thresholds θ(v)≤2 for each vertex v in G, then the problem can be solved in linear time. For a Hamming graph G having thresholds θ(v)=2 for each vertex v of G, we precisely determine an optimal target set S for (G,θ). These results partially answer an open problem raised by Dreyer and Roberts (Discrete Appl. Math. 157:1615–1627, 2009).     

Shifting strategy for geometric graphs without?geometry

We give a simple framework which is an alternative to the celebrated and widely used shifting strategy of Hochbaum and Maass (J. ACM 32(1):103?C136, 1985) which has yielded efficient algorithms with good approximation bounds for numerous optimization problems in low-dimensional Euclidean space. Our framework does not require the input graph/metric to have a geometric realization??it only requires that the input graph satisfy some weak property referred to as growth boundedness. Growth bounded graphs form an important graph class that has been used to model wireless networks. We show how to apply the framework to obtain a polynomial time approximation scheme (PTAS) for the maximum (weighted) independent set problem on this important graph class; the problem is W[1]-complete. Via a more sophisticated application of our framework, we show how to obtain a PTAS for the maximum (weighted) independent set for intersection graphs of (low-dimensional) fat objects that are expressed without geometry. Erlebach et al. (SIAM J. Comput. 34(6):1302?C1323, 2005) and Chan (J. Algorithms 46(2):178?C189, 2003) independently gave a PTAS for maximum weighted independent set problem for intersection graphs of fat geometric objects, say ball graphs, which required a geometric representation of the input. Our result gives a positive answer to a question of Erlebach et al. (SIAM J. Comput. 34(6):1302?C1323, 2005) who asked if a PTAS for this problem can be obtained without access to a geometric representation.     

Women on boards and firm performance

This study investigates the financial performance of Dutch companies both with and without women on their boards. The analysis extends earlier methods used in research by Catalyst (The bottom line: corporate performance and women’s representation on boards, 2007) and McKinsey (Women matter. Gender diversity, a corporate performance driver. McKinsey & Company, USA, 2007), two studies that are often cited in the literature, although, each has a number of methodological shortcomings. This article adds to the international debate, which is often normative, through examining 99 listed companies in the Dutch Female Board Index. Our results show that firms with women directors perform better than those without women on their boards.     

Chromatic number of distance graphs generated by the sets {2,3,x,y}

Let D be a set of positive integers. The distance graph generated by D has all integers ? as the vertex set; two vertices are adjacent whenever their absolute difference falls in D. We completely determine the chromatic number for the distance graphs generated by the sets D={2,3,x,y} for all values x and y. The methods we use include the density of sequences with missing differences and the parameter involved in the so called “lonely runner conjecture”. Previous results on this problem include: For x and y being prime numbers, this problem was completely solved by Voigt and Walther (Discrete Appl. Math. 51:197–209, 1994); and other results for special integers of x and y were obtained by Kemnitz and Kolberg (Discrete Math. 191:113–123, 1998) and by Voigt and Walther (Discrete Math. 97:395–397, 1991).     

Efficient polynomial-time algorithms for the constrained LCS problem with strings exclusion

In this paper, we revisit a recent variant of the longest common subsequence (LCS) problem, the string-excluding constrained LCS (STR-EC-LCS) problem, which was first addressed by Chen and Chao (J Comb Optim 21(3):383–392, 2011). Given two sequences \(X\) and \(Y\) of lengths \(m\) and \(n,\) respectively, and a constraint string \(P\) of length \(r,\) we are to find a common subsequence \(Z\) of \(X\) and \(Y\) which excludes \(P\) as a substring and the length of \(Z\) is maximized. In fact, this problem cannot be correctly solved by the previously proposed algorithm. Thus, we give a correct algorithm with \(O(mnr)\) time to solve it. Then, we revisit the STR-EC-LCS problem with multiple constraints \(\{ P_1, P_2, \ldots , P_k \}.\) We propose a polynomial-time algorithm which runs in \(O(mnR)\) time, where \(R = \sum _{i=1}^{k} |P_i|,\) and thus it overthrows the previous claim of NP-hardness.     

Sustaining Cross-Sector Collaborations: Lessons from New Orleans

This study examines the role of faith-based and nonprofit organizations in cross-sector collaborations and the outcomes of collaborative efforts in one poverty stricken New Orleans neighborhood. The study focuses on a particular one-stop human services center that was established in the target neighborhood post-Hurricane Katrina and was tested during the aftermath of Hurricanes Gustav and Ike. The Center was evaluated during the fall of 2008, to determine whether it held up in achieving relief, recovery and rebuilding efforts, especially in relation to additional needs generated by the more recent storms. Using the Bryson et al. (2006) model of cross-sector collaboration as a beginning framework, and the subsequent expanded model of that same framework from Simo and Bies (2007), the current study examines the successes and current challenges of this particular collaborative organization, analyzes the application of the identified cross-sector collaboration models, defines the role of faith-based organizations and explores the implications for future policy and practice, as well as directions for further research in this important and under-researched area.     

Equivalence of two conjectures on equitable coloring of graphs

A graph G is said to be equitably k-colorable if there exists a proper k-coloring of G such that the sizes of any two color classes differ by at most one. Let Δ(G) denote the maximum degree of a vertex in G. Two Brooks-type conjectures on equitable Δ(G)-colorability have been proposed in Chen and Yen (Discrete Math., 2011) and Kierstead and Kostochka (Combinatorica 30:201–216, 2010) independently. We prove the equivalence of these conjectures.     

(p,q)-total labeling of complete graphs

Given a graph G and positive integers p,q with p≥q, the (p,q)-total number $\lambda_{p,q}^{T}(G)$ of G is the width of the smallest range of integers that suffices to label the vertices and the edges of G such that the labels of any two adjacent vertices are at least q apart, the labels of any two adjacent edges are at least q apart, and the difference between the labels of a vertex and its incident edges is at least p. Havet and Yu (Discrete Math 308:496–513, 2008) first introduced this problem and determined the exact value of $\lambda_{p,1}^{T}(K_{n})$ except for even n with p+5≤n≤6p ²?10p+4. Their proof for showing that $\lambda _{p,1}^{T}(K_{n})\leq n+2p-3$ for odd n has some mistakes. In this paper, we prove that if n is odd, then $\lambda_{p}^{T}(K_{n})\leq n+2p-3$ if p=2, p=3, or $4\lfloor\frac{p}{2}\rfloor+3\leq n\leq4p-1$ . And we extend some results that were given in Havet and Yu (Discrete Math 308:496–513, 2008). Beside these, we give a lower bound for $\lambda_{p,q}^{T}(K_{n})$ under the condition that q<p<2q.     

Adjacent vertex-distinguishing edge coloring of graphs with maximum degree Δ

An adjacent vertex-distinguishing edge coloring, or avd-coloring, of a graph G is a proper edge coloring of G such that no pair of adjacent vertices meets the same set of colors. Let $\operatorname {mad}(G)$ and Δ(G) denote the maximum average degree and the maximum degree of a graph G, respectively. In this paper, we prove that every graph G with Δ(G)≥5 and $\operatorname{mad}(G) < 3-\frac {2}{\Delta}$ can be avd-colored with Δ(G)+1 colors. This completes a result of Wang and Wang (J. Comb. Optim. 19:471–485, 2010).